

def 					_UpperCAmelCase				(						a__ = 6_0_0_8_5_1_4_7_5_1_4_3):

			'''simple docstring'''



			try:
						a_						:						int 							= int(a__)
			except (TypeError, ValueError):
						raise TypeError("""Parameter n must be int or castable to int.""")
			if n <= 0:
						raise ValueError("""Parameter n must be greater than or equal to one.""")
			a_						:						str 							= 2
			a_						:						str 							= 0
			if n == 2:
						return 2
			while n > 2:
						while n % i != 0:
									i += 1
						a_						:						List[Any] 							= i
						while n % i == 0:
									a_						:						str 							= n // i
						i += 1
			return int(a__)


if __name__ == "__main__":
	print(F"""{solution() = }""")





import unittest

from parameterized import parameterized

from transformers import OpenLlamaConfig, is_torch_available, set_seed
from transformers.testing_utils import require_torch, torch_device

from ...generation.test_utils import GenerationTesterMixin
from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, ids_tensor, random_attention_mask
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
	import torch

	from transformers import OpenLlamaForCausalLM, OpenLlamaForSequenceClassification, OpenLlamaModel



class        A__:
						"""simple docstring"""






						def __init__(    self  ,      _lowercase  ,      _lowercase=13  ,      _lowercase=7  ,      _lowercase=True  ,      _lowercase=True  ,      _lowercase=False  ,      _lowercase=True  ,      _lowercase=99  ,      _lowercase=32  ,      _lowercase=5  ,      _lowercase=4  ,      _lowercase=37  ,      _lowercase="gelu"  ,      _lowercase=0.1  ,      _lowercase=0.1  ,      _lowercase=512  ,      _lowercase=16  ,      _lowercase=2  ,      _lowercase=0.0_2  ,      _lowercase=3  ,      _lowercase=4  ,      _lowercase=None  ,      )     -> Tuple:
									a_						:						Union[str, Any] 							= parent
									a_						:						int 							= batch_size
									a_						:						int 							= seq_length
									a_						:						int 							= is_training
									a_						:						List[Any] 							= use_input_mask
									a_						:						str 							= use_token_type_ids
									a_						:						List[str] 							= use_labels
									a_						:						List[Any] 							= vocab_size
									a_						:						Dict 							= hidden_size
									a_						:						List[Any] 							= num_hidden_layers
									a_						:						str 							= num_attention_heads
									a_						:						str 							= intermediate_size
									a_						:						Optional[int] 							= hidden_act
									a_						:						Optional[int] 							= hidden_dropout_prob
									a_						:						int 							= attention_probs_dropout_prob
									a_						:						List[str] 							= max_position_embeddings
									a_						:						Optional[Any] 							= type_vocab_size
									a_						:						Any 							= type_sequence_label_size
									a_						:						List[Any] 							= initializer_range
									a_						:						List[str] 							= num_labels
									a_						:						Union[str, Any] 							= num_choices
									a_						:						Dict 							= scope





						def 			UpperCamelCase__					(    self    )     -> Any:
									a_						:						Dict 							= ids_tensor([self.batch_size, self.seq_length]  ,      self.vocab_size    )

									a_						:						Union[str, Any] 							= None
									if self.use_input_mask:
												a_						:						Optional[int] 							= random_attention_mask([self.batch_size, self.seq_length]    )

									a_						:						List[Any] 							= None
									if self.use_token_type_ids:
												a_						:						Any 							= ids_tensor([self.batch_size, self.seq_length]  ,      self.type_vocab_size    )

									a_						:						Union[str, Any] 							= None
									a_						:						Dict 							= None
									a_						:						Any 							= None
									if self.use_labels:
												a_						:						Tuple 							= ids_tensor([self.batch_size]  ,      self.type_sequence_label_size    )
												a_						:						Optional[int] 							= ids_tensor([self.batch_size, self.seq_length]  ,      self.num_labels    )
												a_						:						int 							= ids_tensor([self.batch_size]  ,      self.num_choices    )

									a_						:						Optional[int] 							= self.get_config()

									return config, input_ids, token_type_ids, input_mask, sequence_labels, token_labels, choice_labels





						def 			UpperCamelCase__					(    self    )     -> Any:
									return OpenLlamaConfig(
									    vocab_size=self.vocab_size  ,      hidden_size=self.hidden_size  ,      num_hidden_layers=self.num_hidden_layers  ,      num_attention_heads=self.num_attention_heads  ,      intermediate_size=self.intermediate_size  ,      hidden_act=self.hidden_act  ,      hidden_dropout_prob=self.hidden_dropout_prob  ,      attention_probs_dropout_prob=self.attention_probs_dropout_prob  ,      max_position_embeddings=self.max_position_embeddings  ,      type_vocab_size=self.type_vocab_size  ,      is_decoder=_lowercase  ,      initializer_range=self.initializer_range  ,      use_stable_embedding=_lowercase  ,      )





						def 			UpperCamelCase__					(    self  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase    )     -> Dict:
									a_						:						Optional[Any] 							= OpenLlamaModel(config=_lowercase    )
									model.to(_lowercase    )
									model.eval()
									a_						:						List[Any] 							= model(_lowercase  ,      attention_mask=_lowercase    )
									a_						:						Optional[Any] 							= model(_lowercase    )
									self.parent.assertEqual(result.last_hidden_state.shape  ,      (self.batch_size, self.seq_length, self.hidden_size)    )





						def 			UpperCamelCase__					(    self  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      )     -> Union[str, Any]:
									a_						:						int 							= True
									a_						:						Union[str, Any] 							= OpenLlamaModel(_lowercase    )
									model.to(_lowercase    )
									model.eval()
									a_						:						Optional[int] 							= model(
									    _lowercase  ,      attention_mask=_lowercase  ,      encoder_hidden_states=_lowercase  ,      encoder_attention_mask=_lowercase  ,      )
									a_						:						Any 							= model(
									    _lowercase  ,      attention_mask=_lowercase  ,      encoder_hidden_states=_lowercase  ,      )
									a_						:						Optional[int] 							= model(_lowercase  ,      attention_mask=_lowercase    )
									self.parent.assertEqual(result.last_hidden_state.shape  ,      (self.batch_size, self.seq_length, self.hidden_size)    )





						def 			UpperCamelCase__					(    self  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      )     -> Any:
									a_						:						Dict 							= OpenLlamaForCausalLM(config=_lowercase    )
									model.to(_lowercase    )
									model.eval()
									a_						:						int 							= model(_lowercase  ,      attention_mask=_lowercase  ,      labels=_lowercase    )
									self.parent.assertEqual(result.logits.shape  ,      (self.batch_size, self.seq_length, self.vocab_size)    )





						def 			UpperCamelCase__					(    self  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      _lowercase  ,      )     -> List[str]:
									a_						:						Dict 							= True
									a_						:						Optional[int] 							= True
									a_						:						Dict 							= OpenLlamaForCausalLM(config=_lowercase    )
									model.to(_lowercase    )
									model.eval()

									# first forward pass
									a_						:						List[str] 							= model(
									    _lowercase  ,      attention_mask=_lowercase  ,      encoder_hidden_states=_lowercase  ,      encoder_attention_mask=_lowercase  ,      use_cache=_lowercase  ,      )
									a_						:						Optional[Any] 							= outputs.past_key_values

									# create hypothetical multiple next token and extent to next_input_ids
									a_						:						Optional[Any] 							= ids_tensor((self.batch_size, 3)  ,      config.vocab_size    )
									a_						:						Union[str, Any] 							= ids_tensor((self.batch_size, 3)  ,      vocab_size=2    )

									# append to next input_ids and
									a_						:						Any 							= torch.cat([input_ids, next_tokens]  ,      dim=-1    )
									a_						:						Any 							= torch.cat([input_mask, next_mask]  ,      dim=-1    )

									a_						:						Optional[int] 							= model(
									    _lowercase  ,      attention_mask=_lowercase  ,      encoder_hidden_states=_lowercase  ,      encoder_attention_mask=_lowercase  ,      output_hidden_states=_lowercase  ,      )["""hidden_states"""][0]
									a_						:						Dict 							= model(
									    _lowercase  ,      attention_mask=_lowercase  ,      encoder_hidden_states=_lowercase  ,      encoder_attention_mask=_lowercase  ,      past_key_values=_lowercase  ,      output_hidden_states=_lowercase  ,      )["""hidden_states"""][0]

									# select random slice
									a_						:						Optional[int] 							= ids_tensor((1,)  ,      output_from_past.shape[-1]    ).item()
									a_						:						Dict 							= output_from_no_past[:, -3:, random_slice_idx].detach()
									a_						:						Optional[int] 							= output_from_past[:, :, random_slice_idx].detach()

									self.parent.assertTrue(output_from_past_slice.shape[1] == next_tokens.shape[1]    )

									# test that outputs are equal for slice
									self.parent.assertTrue(torch.allclose(_lowercase  ,      _lowercase  ,      atol=1e-3    )    )





						def 			UpperCamelCase__					(    self    )     -> Optional[Any]:
									a_						:						Any 							= self.prepare_config_and_inputs()
									(
									    (
									    a_
									)							,					(
									    a_
									)							,					(
									    a_
									)							,					(
									    a_
									)							,					(
									    a_
									)							,					(
									    a_
									)							,					(
									    a_
									)							,					
									)						:						Union[str, Any] 							= config_and_inputs
									a_						:						Tuple 							= {"""input_ids""": input_ids, """attention_mask""": input_mask}
									return config, inputs_dict







@require_torch
class        A__(a_,  a_,  a_,  unittest.TestCase							):
						"""simple docstring"""






						_A    :				Tuple       					=			(
						    (OpenLlamaModel, OpenLlamaForCausalLM, OpenLlamaForSequenceClassification) if is_torch_available() else ()
						)
						_A    :				int       					=			(OpenLlamaForCausalLM,) if is_torch_available() else ()
						_A    :				Optional[int]       					=			(
						    {
						        '''feature-extraction''': OpenLlamaModel,
						        '''text-classification''': OpenLlamaForSequenceClassification,
						        '''text-generation''': OpenLlamaForCausalLM,
						        '''zero-shot''': OpenLlamaForSequenceClassification,
						    }
						    if is_torch_available()
						    else {}
						)
						_A    :				Tuple       					=			False
						_A    :				Any       					=			False





						def 			UpperCamelCase__					(    self    )     -> List[str]:
									a_						:						Optional[int] 							= OpenLlamaModelTester(self    )
									a_						:						Optional[int] 							= ConfigTester(self  ,      config_class=_lowercase  ,      hidden_size=37    )





						def 			UpperCamelCase__					(    self    )     -> Any:
									self.config_tester.run_common_tests()





						def 			UpperCamelCase__					(    self    )     -> Optional[Any]:
									a_						:						Union[str, Any] 							= self.model_tester.prepare_config_and_inputs()
									self.model_tester.create_and_check_model(*_lowercase    )





						def 			UpperCamelCase__					(    self    )     -> Tuple:
									a_						:						Any 							= self.model_tester.prepare_config_and_inputs()
									for type in ["absolute", "relative_key", "relative_key_query"]:
												a_						:						Dict 							= type
												self.model_tester.create_and_check_model(*_lowercase    )





						def 			UpperCamelCase__					(    self    )     -> Union[str, Any]:
									a_							,					a_						:						Tuple 							= self.model_tester.prepare_config_and_inputs_for_common()
									a_						:						Any 							= 3
									a_						:						List[str] 							= input_dict["""input_ids"""]
									a_						:						List[str] 							= input_ids.ne(1    ).to(_lowercase    )
									a_						:						int 							= ids_tensor([self.model_tester.batch_size]  ,      self.model_tester.type_sequence_label_size    )
									a_						:						int 							= OpenLlamaForSequenceClassification(_lowercase    )
									model.to(_lowercase    )
									model.eval()
									a_						:						Tuple 							= model(_lowercase  ,      attention_mask=_lowercase  ,      labels=_lowercase    )
									self.assertEqual(result.logits.shape  ,      (self.model_tester.batch_size, self.model_tester.num_labels)    )





						def 			UpperCamelCase__					(    self    )     -> Optional[Any]:
									a_							,					a_						:						Any 							= self.model_tester.prepare_config_and_inputs_for_common()
									a_						:						Union[str, Any] 							= 3
									a_						:						List[Any] 							= """single_label_classification"""
									a_						:						Dict 							= input_dict["""input_ids"""]
									a_						:						int 							= input_ids.ne(1    ).to(_lowercase    )
									a_						:						List[str] 							= ids_tensor([self.model_tester.batch_size]  ,      self.model_tester.type_sequence_label_size    )
									a_						:						Any 							= OpenLlamaForSequenceClassification(_lowercase    )
									model.to(_lowercase    )
									model.eval()
									a_						:						Any 							= model(_lowercase  ,      attention_mask=_lowercase  ,      labels=_lowercase    )
									self.assertEqual(result.logits.shape  ,      (self.model_tester.batch_size, self.model_tester.num_labels)    )





						def 			UpperCamelCase__					(    self    )     -> Tuple:
									a_							,					a_						:						Union[str, Any] 							= self.model_tester.prepare_config_and_inputs_for_common()
									a_						:						Any 							= 3
									a_						:						List[str] 							= """multi_label_classification"""
									a_						:						Dict 							= input_dict["""input_ids"""]
									a_						:						Any 							= input_ids.ne(1    ).to(_lowercase    )
									a_						:						List[Any] 							= ids_tensor(
									    [self.model_tester.batch_size, config.num_labels]  ,      self.model_tester.type_sequence_label_size    ).to(torch.float    )
									a_						:						Optional[int] 							= OpenLlamaForSequenceClassification(_lowercase    )
									model.to(_lowercase    )
									model.eval()
									a_						:						int 							= model(_lowercase  ,      attention_mask=_lowercase  ,      labels=_lowercase    )
									self.assertEqual(result.logits.shape  ,      (self.model_tester.batch_size, self.model_tester.num_labels)    )





						@unittest.skip("""Open-Llama buffers include complex numbers, which breaks this test"""    )
						def 			UpperCamelCase__					(    self    )     -> Tuple:
									pass





						@parameterized.expand([("""linear""",), ("""dynamic""",)]    )
						def 			UpperCamelCase__					(    self  ,      _lowercase    )     -> str:
									a_							,					a_						:						Optional[int] 							= self.model_tester.prepare_config_and_inputs_for_common()
									a_						:						List[Any] 							= ids_tensor([1, 10]  ,      config.vocab_size    )
									a_						:						str 							= ids_tensor([1, int(config.max_position_embeddings * 1.5    )]  ,      config.vocab_size    )

									set_seed(42    )  # Fixed seed at init time so the two models get the same random weights
									a_						:						Union[str, Any] 							= OpenLlamaModel(_lowercase    )
									original_model.to(_lowercase    )
									original_model.eval()
									a_						:						Union[str, Any] 							= original_model(_lowercase    ).last_hidden_state
									a_						:						str 							= original_model(_lowercase    ).last_hidden_state

									set_seed(42    )  # Fixed seed at init time so the two models get the same random weights
									a_						:						int 							= {"""type""": scaling_type, """factor""": 1_0.0}
									a_						:						Union[str, Any] 							= OpenLlamaModel(_lowercase    )
									scaled_model.to(_lowercase    )
									scaled_model.eval()
									a_						:						Optional[int] 							= scaled_model(_lowercase    ).last_hidden_state
									a_						:						Tuple 							= scaled_model(_lowercase    ).last_hidden_state

									# Dynamic scaling does not change the RoPE embeddings until it receives an input longer than the original
									# maximum sequence length, so the outputs for the short input should match.
									if scaling_type == "dynamic":
												self.assertTrue(torch.allclose(_lowercase  ,      _lowercase  ,      atol=1e-5    )    )
									else:
												self.assertFalse(torch.allclose(_lowercase  ,      _lowercase  ,      atol=1e-5    )    )

									# The output should be different for long inputs
									self.assertFalse(torch.allclose(_lowercase  ,      _lowercase  ,      atol=1e-5    )    )


